The ArcGIS Server help page Publishing additional services for printing shows how to publish an MXD as a print template:
Navigate to Toolboxes > System Toolboxes > Server Tools > Printing. Double-click the Export Web Map tool. Click Geoprocessing > Results to display the Results window. Right-click the ExportWebMap result and click Share As > Geoprocessing Service.
These instructions seem to apply to ArcGIS Server only. How can I use a print template, derived from an MXD, within ArcGIS Online?
(The question Setting up ArcGIS Print service for ArcGIS Online account? shows that ArcGIS Online supports a print service, but doesn't confirm that ArcGIS Online supports a custom template derived from ArcMap.)